Discussions On A-Lie Group And Related Operators

A-manifold is a natural generalization of the concept of manifold. Then A-lie group can also be regarded as the natural generalization of the concept of lie group. But just as we know, they also have many characteristics of bundles and algebra. In this paper, we did some researches on its basic properties in terms of .A-lie group by introducing the concept of both A-lie group metahomomorphism and complex poisson affine group.And we hope to deepen our comprehension of A-lie group. This paper was divided into the following two parts:Part 1. Discussion on A-lie group;Part 2. Discussion on two special kinds of A-manifold.In the section 1.1, we mainly research the intersection of A-lie groups and the product of A-lie groups, ect. By defining A-lie group metahomomorphism we discuss some properties about A-lie group metahomomorphism, and then we get some good conclusions in the section 1.2. In the Part 2 two special kinds of A-manifolds are discussed. In the section 2.1, the relations among pull-back operator F~*, retraction operator i_X,i_Y and lie derivative L_X ,L_Y are given. By studying the concept of complex poisson affine group its sufficient and necessary condition is given in last section.